Certificate for #20046 ⟨a, b | aab=a, bbbb=bba⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = 0; deg(b) = 1

Axiom: aab=a.

Referenced by [3], [5], [6], [7].

Axiom: bbbb=bba.

Defines rule #4.

Referenced by [3], [4].

Overlap of [1] aab=a with [2] bbbb=bba:

Critical pair: aabba=abbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [7].

Overlap of [2] bbbb=bba with [2] bbbb=bba:

Critical pair: bbba=bbab.

Flip LHS and RHS.

Referenced by [8].

Overlap of [1] aab=a with [3] abbb=aba:

Critical pair: aaba=abb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [1] aab=a with [5] abb=aa:

Critical pair: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8].

Overlap of [3] abbb=aba with [5] abb=aa:

Critical pair: aab=aba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [4] bbab=bbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.